Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
782 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19098355 | C2 | semidirect |
| 3. #23763318 | C2 | semidirect |
| 4. #23761524 | C2 | semidirect |
| 5. C2×#410×C79 | C2 | semidirect |
| 7. C2×#14579150 | C4 | semidirect |
| 8. C2×#14579135 | C4 | semidirect |
| 13. #19098470 | C4 | semidirect |
| 18. C4×C22⋊Dic79 | C4 | semidirect |
| 71. #99×C79 | D4 | semidirect |
| 266. C2×#410 | D79 | semidirect |
| 271. C79 | #13089 | semidirect |
| 332. #99 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23767015 | 2 |
| C2×#19098355 | 2 |
| #23763318 | 2 |
| #23761524 | 2 |
| C2×#410×C79 | 2 |
| #13089 | 79 |